Question

(a+b)^3 = a^3+3a^2b+3ab^2+b^3

right or wrong ​

Answer 1

Yeah it's right ✔️

♦ Proof :-

As we know that,

→ ( a + b )³ can be written as ( a + b ) ( a + b ) ( a + b )

Now simplifying it we have ,

⇒ ( a² + b² + 2ab ) ( a + b )

Substituting 2ab = ab + ab

⇒ ( a² + b² + ab + ab ) ( a + b )

⇒ a³ + a²b + b²a + b³ + a²b + ab² + a²b + ab²

⇒ a³ + b³ + 3a²b + 3ab² .....[ Hence proved ! ]

It can also be written as a³ + b³ + 3ab ( a + b )

Hence , it is right

More information :-

Algebraic identities ,

• ( a + b )² = a² + b² + 2ab
• ( a - b )² = a² + b² - 2ab
• ( a + b ) ( a - b ) = a² - b²
• ( a + b )² - 2ab = a² + b²

Answer 2

Answer:

⚡Yeah it is right⚡.

Proof;

(a+b)^3=(a+b)(a+b)(a+b)

After simplifying this we get;

(a^2+b^2+2ab)(a+b).

Substituting 2ab=ab+ab.

(a^2+b^2+ab+ab)(a+b)

= a^3+ab^2+a^2b+a^2b+a^2b+b^3+b^2a+b^2a

=a^3+b^3+3a^b+3ab^2.

HENCE, (PROVED).